Rewrite as a simplified fraction. ${3.\overline{1} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 31.1111...\\ 1x &= 3.1111...\end{align*}}$ Subtracting the two equations, we have: ${9x = 28}$ ${x = \dfrac{28}{9}} \text{or} {3 \dfrac{1}{9}}$